Poisson Noise Research Articles

Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise

In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by k-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.

Photon Statistics Modal Reconstruction by Detected and Undetected Light

AbstractA novel technique is introduced for the reconstruction of multimode optical fields, based on simultaneously exploiting both the generalized Glauber's Kth‐order correlation function and a recently proposed anti‐correlation function (dubbed ) which is resilient to Poissonian noise. It is experimentally demonstrated that this method yields mode reconstructions with higher fidelity with respect to those obtained with reconstruction methods based only on 's, even requiring less “a priori” information. The reliability and versatility of this technique make it suitable for a widespread use in real applications of optical quantum measurement, from quantum information to quantum metrology, especially when one needs to characterize ensembles of single‐photon emitters in the presence of background noise (due, for example, to residual excitation laser, stray light or unwanted fluorescence).

Comparison of denoising tools for the reconstruction of nonlinear multimodal images.

Biophotonic multimodal imaging techniques provide deep insights into biological samples such as cells or tissues. However, the measurement time increases dramatically when high-resolution multimodal images (MM) are required. To address this challenge, mathematical methods can be used to shorten the acquisition time for such high-quality images. In this research, we compared standard methods, e.g., the median filter method and the phase retrieval method via the Gerchberg-Saxton algorithm with artificial intelligence (AI) based methods using MM images of head and neck tissues. The AI methods include two approaches: the first one is a transfer learning-based technique that uses the pre-trained network DnCNN. The second approach is the training of networks using augmented head and neck MM images. In this manner, we compared the Noise2Noise network, the MIRNet network, and our deep learning network namely incSRCNN, which is derived from the super-resolution convolutional neural network and inspired by the inception network. These methods reconstruct improved images using measured low-quality (LQ) images, which were measured in approximately 2 seconds. The evaluation was performed on artificial LQ images generated by degrading high-quality (HQ) images measured in 8 seconds using Poisson noise. The results showed the potential of using deep learning on these multimodal images to improve the data quality and reduce the acquisition time. Our proposed network has the advantage of having a simple architecture compared with similar-performing but highly parametrized networks DnCNN, MIRNet, and Noise2Noise.

Speckle noise removal via learned variational models

In this paper, we address the image denoising problem in presence of speckle degradation typically arising in ultra-sound images. Variational methods and Convolutional Neural Networks (CNNs) are considered well-established methods for specific noise types, such as Gaussian and Poisson noise. Nonetheless, the advances achieved by these two classes of strategies are limited when tackling the de-speckle problem. In fact, variational methods for speckle removal typically amounts to solve a non-convex functional with the related issues from the convergence viewpoint; on the other hand, the lack of large datasets of noise-free ultra-sound images has not allowed the extension of the state-of-the-art CNN denoiser methods to the case of speckle degradation. Here, we aim at combining the classical variational methods with the predictive properties of CNNs by considering a weighted total variation regularized model; the local weights are obtained as the output of a statistically inspired neural network that is trained on a small and composite dataset of natural and synthetic images. The resulting non-convex variational model, which is minimized by means of the Alternating Direction Method of Multipliers (ADMM) is proven to converge to a stationary point. Numerical tests show the effectiveness of our approach for the denoising of natural and satellite images.

Coronal height constraint in IRAS 13224–3809 and 1H 0707–495 by the random forest regressor

ABSTRACT We develop a random forest regressor (RFR) machine learning model to trace the coronal evolution in two highly variable active galactic nuclei (AGNs) IRAS 13224-3809 and 1H 0707-495 observed with XMM–Newton, by probing the X-ray reverberation features imprinted on their power spectral density (PSD) profiles. Simulated PSDs in the form of a power law, with a similar frequency range and bins to the observed data, are produced. Then, they are convolved with relativistic disc-response functions from a lamp-post source before being used to train and test the model to predict the coronal height. We remove some bins that are dominated by Poisson noise and find that the model can tolerate the frequency-bin removal up to ∼10 bins to maintain a prediction accuracy of R2 > 0.9. The black hole mass and inclination should be fixed so that the accuracy in predicting the source height is still >0.9. The accuracy also increases with the reflection fraction. The corona heights for both AGN are then predicted using the RFR model developed from the simulated PSDs, whose frequency range and bins are specifically adjusted to match those from each individual observation. The model suggests that their corona varies between ∼5–18 rg, with R2 > 0.9 for all observations. Such high accuracy can still be obtained if the difference between the true mass and the trained value is ${\lesssim}10\ \hbox{per cent}$. Finally, the model supports the height-changing corona under the light-bending scenario, where the height is correlated to source luminosity in both IRAS 13224-3809 and 1H 0707-495.

Poisson Noise Reduction with Nonlocal-PCA Hybrid Model in Medical X-ray Images

The presence of Poisson noise in medical X-ray images leads to degradation of the image quality. The obscured information is required for accurate diagnosis. During X-ray image acquisition process, weak light results into limited number of available photons, which leads into the Poisson noise commonly known as X-ray noise. Currently, the available X-ray noise removal methods have not yet obtained satisfying total denoising results to remove noise from the medical X-ray images. The available techniques tend to show good performance when the image model corresponds to the algorithm’s assumptions used but in general, the denoising algorithms fail to do complete denoise. X-ray image quality could be improved by increasing the X-ray dose value (beyond the maximum medically permissible dose) but the process could be lethal to patients’ health since higher X-ray energy may kill cells due to the effects of higher dose values. In this study, the hybrid model that combines the Poisson Principal Component Analysis (Poisson PCA) with the nonlocal (NL) means denoising algorithm is developed to reduce noise in images. This hybrid model for X-ray noise removal and the contrast enhancement improves the quality of X-ray images and can, thus, be used for medical diagnosis. The performance of the proposed hybrid model was observed by using the standard data and was compared with the standard Poisson algorithms.

Local optimized Stokes polarimetry for specific polarization states.

In this Letter, we propose a locally optimized Stokes polarimetry. Focusing on the effect on polarization measurements by Poisson noise, the studies establish a new, to the best of our knowledge, optimization function combining the equally weighted variance with the condition number. This method considers both the stability and the precision of polarization measurements; by trading an increase in the condition number by 2.48%, we realize a decrease in equal-weighted variance by 19.1% near the north pole. The advantages of this local optimization method are demonstrated based on Monte Carlo (MC) simulations and experiments of continuous polarization state modulation. Finally, an imaging demonstration using a 4 µm pathological section implies the potential of this new local optimization method in improving polarization measurements and applying it to more biomedical research.

The magnetohydrodynamic-particle-in-cell module in athena++: implementation and code tests

ABSTRACT We present a new magnetohydrodynamic-particle-in-cell (MHD-PIC) code integrated into the athena++ framework. It treats energetic particles as in conventional PIC codes, while the rest of thermal plasmas are treated as background fluid described by MHD, thus primarily targeting at multiscale astrophysical problems involving the kinetic physics of the cosmic rays (CRs). The code is optimized towards efficient vectorization in interpolation and particle deposits, with excellent parallel scaling. The code is also compatible with static/adaptive mesh refinement, with dynamic load balancing to further enhance multiscale simulations. In addition, we have implemented a compressing/expanding box framework that allows adiabatic driving of CR pressure anisotropy, as well as the δf method that can dramatically reduce Poisson noise in problems where distribution function f is only expected to slightly deviate from the background. The code performance is demonstrated over a series of benchmark test problems, including particle acceleration in non-relativistic parallel shocks. In particular, we reproduce the linear growth of the CR gyro-resonant (streaming and pressure anisotropy) instabilities, under both the periodic and expanding/compressing box settings. We anticipate the code to open up the avenue for a wide range of astrophysical and plasma physics applications.

NON-CONVEX HYBRID TOTAL VARIATION FOR RESTORING MEDICAL IMAGE CORRUPTED BY POISSON NOISE

Abstract. In this work, we proposed the hybrid non-convex regularizers for Poisson noise removal on medical images. The model is built by a combination of non-convex total variation and non-convex fractional total variation. The proposed model allows for avoiding the annoying staircase artifacts and obtaining the reconstruction results with sharp and neat edges during the noise removal process. For handling the minimization problem, we employ the alternating minimization method associated with the iteratively reweighted l1 algorithm. Numerical experiments illustrate the efficiency of the proposed model and corresponding algorithm.

Deep learning methods for noisy sperm image classification from convolutional neural network to visual transformer: a comprehensive comparative study

Background With the gradual increase of infertility in the world, among which male sperm problems are the main factor for infertility, more and more couples are using computer-assisted sperm analysis (CASA) to assist in the analysis and treatment of infertility. Meanwhile, the rapid development of deep learning (DL) has led to strong results in image classification tasks. However, the classification of sperm images has not been well studied in current deep learning methods, and the sperm images are often affected by noise in practical CASA applications. The purpose of this article is to investigate the anti-noise robustness of deep learning classification methods applied on sperm images.Methods The SVIA dataset is a publicly available large-scale sperm dataset containing three subsets. In this work, we used subset-C, which provides more than 125,000 independent images of sperms and impurities, including 121,401 sperm images and 4,479 impurity images. To investigate the anti-noise robustness of deep learning classification methods applied on sperm images, we conducted a comprehensive comparative study of sperm images using many convolutional neural network (CNN) and visual transformer (VT) deep learning methods to find the deep learning model with the most stable anti-noise robustness.Results This study proved that VT had strong robustness for the classification of tiny object (sperm and impurity) image datasets under some types of conventional noise and some adversarial attacks. In particular, under the influence of Poisson noise, accuracy changed from 91.45% to 91.08%, impurity precison changed from 92.7% to 91.3%, impurity recall changed from 88.8% to 89.5%, and impurity F1-score changed 90.7% to 90.4%. Meanwhile, sperm precision changed from 90.9% to 90.5%, sperm recall changed from 92.5% to 93.8%, and sperm F1-score changed from 92.1% to 90.4%.Conclusion Sperm image classification may be strongly affected by noise in current deep learning methods; the robustness with regard to noise of VT methods based on global information is greater than that of CNN methods based on local information, indicating that the robustness with regard to noise is reflected mainly in global information.

Fractional-Order Variational Image Fusion and Denoising Based on Data-Driven Tight Frame

Multi-modal image fusion can provide more image information, which improves the image quality for subsequent image processing tasks. Because the images acquired using photon counting devices always suffer from Poisson noise, this paper proposes a new three-step method based on the fractional-order variational method and data-driven tight frame to solve the problem of multi-modal image fusion for images corrupted by Poisson noise. Thus, this article obtains fused high-quality images while removing Poisson noise. The proposed image fusion model can be solved by the split Bregman algorithm which has significant stability and fast convergence. The numerical results on various modal images show the excellent performance of the proposed three-step method in terms of numerical evaluation metrics and visual quality. Extensive experiments demonstrate that our method outperforms state-of-the-art methods on image fusion with Poisson noise.

De-Noising of Photoacoustic Microscopy Images by Attentive Generative Adversarial Network.

As a hybrid imaging technology, photoacoustic microscopy (PAM) imaging suffers from noise due to the maximum permissible exposure of laser intensity, attenuation of ultrasound in the tissue, and the inherent noise of the transducer. De-noising is an image processing method to reduce noise, and PAM image quality can be recovered. However, previous de-noising techniques usually heavily rely on manually selected parameters, resulting in unsatisfactory and slow de-noising performance for different noisy images, which greatly hinders practical and clinical applications. In this work, we propose a deep learning-based method to remove noise from PAM images without manual selection of settings for different noisy images. An attention enhanced generative adversarial network is used to extract image features and adaptively remove various levels of Gaussian, Poisson, and Rayleigh noise. The proposed method is demonstrated on both synthetic and real datasets, including phantom (leaf veins) and in vivo (mouse ear blood vessels and zebrafish pigment) experiments. In the in vivo experiments using synthetic datasets, our method achieves the improvement of 6.53 dB and 0.26 in peak signal-to-noise ratio and structural similarity metrics, respectively. The results show that compared with previous PAM de-noising methods, our method exhibits good performance in recovering images qualitatively and quantitatively. In addition, the de-noising processing speed of 0.016 s is achieved for an image with 256×256 pixels, which has the potential for real-time applications. Our approach is effective and practical for the de-noising of PAM images.

ELFPIE: an error-laxity Fourier ptychographic iterative engine

We present a simple but efficient and robust reconstruction algorithm for Fourier ptychographic microscopy, termed error-laxity Fourier ptychographic iterative engine (Elfpie), that is simultaneously robust to (1) noise signal (including Gaussian, Poisson, and salt & pepper noises), (2) problematic background illumination problem, (3) vignetting effects and (4) misaligning of LED positions, without the need of calibrating or recovering these system errors. In Elfpie, we embed the inverse problem of FPM under the framework of feature extraction/recovering and propose a new image gradient-based data fidelity cost function regularized by the global second-order total-variation regularization. The closed-form complex gradient for the cost function is derived and is back-propagated using the AdaBelief optimizer with an adaptive learning rate. The Elfpie was tested on both simulation and experimental data. In general, compared against SOTA methods, the Elfpie is robust to Gaussian noise with a 100 times larger noise, salt & pepper noise with 1000 times larger noise and Poisson noise with 10 times larger noise. The Elfpie is able to reconstruct high-fidelity samples under LED position misalignments up to 2 mm. It can also bypass the vignetting effect, for which all SOTA methods fail to reconstruct the sample pattern. The MATLAB code for ELFPIE is available on Github.

Noise Estimation and Type Identification in Natural Scene and Medical Images using Deep Learning Approaches

The image enhancement for the natural images is the vast field where the quality of the images degrades based on the capturing and processing methods employed by the capturing devices. Based on noise type and estimation of noise, filter need to be adopted for enhancing the quality of the image. In the same manner, the medical field also needs some filtering mechanism to reduce the noise and detection of the disease based on the clarity of the image captured; in accordance with it, the preprocessing steps play a vital role to reduce the burden on the radiologist to make the decision on presence of disease. Based on the estimated noise and its type, the filters are selected to delete the unwanted signals from the image. Hence, identifying noise types and denoising play an important role in image analysis. The proposed framework addresses the noise estimation and filtering process to obtain the enhanced images. This paper estimates and detects the noise types, namely Gaussian, motion artifacts, Poisson, salt-andpepper, and speckle noises. Noise is estimated by using discrete wavelet transformation (DWT). This separates the image into quadruple sub-bands. Noise and HH sub-band are high-frequency components. HH sub-band also has vertical edges. These vertical edges are removed by performing Hadamard operation on downsampled Sobel edge-detected image and HH sub-band. Using HH sub-band after removing vertical edges is considered for estimating the noise. The Rician energy equation is used to estimate the noise. This is given as input for Artificial Neural Network to improve the estimated noise level. For identifying noise type, CNN is used. After removing vertical edges, the HH sub-band is given to the CNN model for classification. The classification accuracy results of identifying noise type are 100% on natural images and 96.3% on medical images.

A novel CT image de-noising and fusion based deep learning network to screen for disease (COVID-19)

A COVID-19, caused by SARS-CoV-2, has been declared a global pandemic by WHO. It first appeared in China at the end of 2019 and quickly spread throughout the world. During the third layer, it became more critical. COVID-19 spread is extremely difficult to control, and a huge number of suspected cases must be screened for a cure as soon as possible. COVID-19 laboratory testing takes time and can result in significant false negatives. To combat COVID-19, reliable, accurate and fast methods are urgently needed. The commonly used Reverse Transcription Polymerase Chain Reaction has a low sensitivity of approximately 60% to 70%, and sometimes even produces negative results. Computer Tomography (CT) has been observed to be a subtle approach to detecting COVID-19, and it may be the best screening method. The scanned image's quality, which is impacted by motion-induced Poisson or Impulse noise, is vital. In order to improve the quality of the acquired image for post segmentation, a novel Impulse and Poisson noise reduction method employing boundary division max/min intensities elimination along with an adaptive window size mechanism is proposed. In the second phase, a number of CNN techniques are explored for detecting COVID-19 from CT images and an Assessment Fusion Based model is proposed to predict the result. The AFM combines the results for cutting-edge CNN architectures and generates a final prediction based on choices. The empirical results demonstrate that our proposed method performs extensively and is extremely useful in actual diagnostic situations.

Quantum transport and shot noise in two-dimensional semi-Dirac system

Two-dimensional (2D) semi-Dirac systems, such as 2D black phosphorus and arsenene, can exhibit a rich topological phase transition between insulating, semi-Dirac, and band inversion phases when subjected to an external modulation. How these phase transitions manifest within the quantum transport and shot noise signatures remains an open question thus far. Here, we show that the Fano factor converges to the universal F ≈ 0.179 at the semi-Dirac phase and transits between the sub-Poissonian ( F ≈ 1 / 3) and the Poissonian shot noise ( F ≈ 1) limit at the band inversion and the insulating phase, respectively. Furthermore, the conductance of a 2D semi-Dirac system converges to the contrasting limit of G / G 0 → 1 / d and G / G 0 → 0 at the band inversion and the insulating phases, respectively. The quantum tunneling spectra exhibits a peculiar coexistence of massless and massive Dirac quasiparticles in the band inversion regime, thus providing a versatile sandbox to study the tunneling behavior of various Dirac quasiparticles. These findings reveal the rich interplay between band topology and quantum transport signatures, which may serve as smoking gun signatures for the experimental studies of semi-Dirac systems near the topological phase transition.

Low-dose imaging denoising with one pair of noisy images.

Low-dose imaging techniques have many important applications in diverse fields, from biological engineering to materials science. Samples can be protected from phototoxicity or radiation-induced damage using low-dose illumination. However, imaging under a low-dose condition is dominated by Poisson noise and additive Gaussian noise, which seriously affects the imaging quality, such as signal-to-noise ratio, contrast, and resolution. In this work, we demonstrate a low-dose imaging denoising method that incorporates the noise statistical model into a deep neural network. One pair of noisy images is used instead of clear target labels and the parameters of the network are optimized by the noise statistical model. The proposed method is evaluated using simulation data of the optical microscope, and scanning transmission electron microscope under different low-dose illumination conditions. In order to capture two noisy measurements of the same information in a dynamic process, we built an optical microscope that is capable of capturing a pair of images with independent and identically distributed noises in one shot. A biological dynamic process under low-dose condition imaging is performed and reconstructed with the proposed method. We experimentally demonstrate that the proposed method is effective on an optical microscope, fluorescence microscope, and scanning transmission electron microscope, and show that the reconstructed images are improved in terms of signal-to-noise ratio and spatial resolution. We believe that the proposed method could be applied to a wide range of low-dose imaging systems from biological to material science.

Inversion of Wind and Temperature from Low SNR FPI Interferograms

The temperature and wind in the middle and upper atmosphere can be obtained by recording the Doppler shift and broadening of the airglow emission, which is reflected by the interference ring from a ground-based Fabry–Perot interferometer (FPI) system. FPI observations are highly susceptible to weather and the external environment, which seriously affect the signal-to-noise ratio (SNR) of FPI interferograms. An SNR can significantly increase errors in determining the center of the interferogram, leading to inaccurate wind and temperature inversions. The calculation shows that the wind inversion from the interferogram decreases and the temperature increases for larger central errors. In this paper, we propose the maximum standard deviation method (MSDM) with high accuracy and robustness to determine the interference ring center. The performance of the MSDM is better achieved by using more than 100 1D interferogram bins to determine the center of interferograms. The robustness of the MSDM is investigated by computing numerous simulated interferograms with white Gaussian noise and Poisson noise, and compared with the two algorithms of binarization and peak fitting, which are usually used to invert wind and temperature from the interference ring of FPI. The results show that MSDM has higher accuracy and robustness than the other two algorithms. We also simulate the distortion interferogram when the FPI may be illuminated by inhomogeneous background light, which can introduce additional errors in wind and temperature, and the MSDM still performs better. Finally, we invert the wind and temperature from the real airglow interferogram by the Kelan (38.7°N, 111.6°E) FPI, which shows that both the wind and temperature inverted by MSDM better agree well with the FPI product than the other two algorithms. Therefore, the MSDM helps to improve the accuracy and stability to invert the wind and temperature.

Extremely Weak Signal Detection Algorithm of Multi-Pixel Photon Detector

For the detection of extremely weak signals in underwater long distance wireless optical communication, the Geiger mode of the multi pixel photon detector has serious pulse superposition effect and Poisson noise, which leads to counting difficulties and affects the measurement accuracy. This paper proposes a deconvolution joint generalized Anscombe transform (DUGAT) detection algorithm. First, the deconvolution filtering technology is used to process the weak signal to reduce the superposition effect and converge the pulse width. Secondly, the noise signal of Poisson+Gaussian (P+G) distribution is converted into Gaussian variable by using generalized Anscombe transform (GAT), which is equivalent to additive Gaussian noise signal. Finally, the symbols are counted by hard decision algorithm. The experimental results show that the sensitivity of this algorithm is improved by 8.57dB and 9.95dB respectively compared with the traditional AR and ML detection algorithms.

A Note on a Strong Persistence of Stochastic Predator-Prey Model with Jumps

We study the non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower term and Holling-type II functional response driven by the system of stochastic differential equations with white noise, centered and non-centered Poisson noises. The sufficient conditions of strong persistence in the mean of the solution to the considered system are obtained.